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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Shear strength of a refractory high entropy alloy MoNbTaVW under high pressure

Radial X-ray diffraction (R-XRD) was performed in situ using a Panoramic Diamond Anvil Cell on the refractory high entropy alloy MoNbTaVW. The lattice parameters were determined through a Le Bail fit using a body centered cubic (BCC) lattice of symmetry $Im$$\overline{3}$$m$ (international space group number 229). Upper and lower bounds to the shear strength were determined up to 80 GPa nonhydrostatically using copper as a pressure standard. The equation of state was derived at the magic angle ψ = 54.7° and yielded a bulk modulus of K 0 = 220.8 ± 1.65 GPa. The experimental lattice parameters and bulk modulus match closely with corresponding density functional theory (DFT) calculations. The BCC phase remains stable up to the highest pressure of 80 GPa studied and is shown to be elastically anisotropic. The shear strength was found to saturate around 70 GPa with a value of τ = 1.75 GPa, and the shear moduli are presented in different limits of iso-strain and iso-stress.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Equations of state, phase relations, and oxygen fugacity of the Ru-RuO 2 buffer at high pressures and temperatures

Experimental studies and measurements of inclusions in diamonds show that ferric iron components are increasingly stabilized with depth in the mantle. To determine the thermodynamic stability of such components, their concentration needs to be measured at known oxygen fugacities. The metal-oxide pair Ru and RuO 2 are ideal as an internal oxygen fugacity buffer in high-pressure experiments. Both phases remain solid to high temperatures and react minimally with silicates, only exchanging oxygen. To calculate oxygen fugacities at high pressure and temperature, however, requires information on the phase relations and equation of state properties of the solid phases. We have made in situ synchrotron X-ray diffraction measurements in a multi-anvil press on mixtures of Ru and RuO 2 to 19.4 GPa and 1473 K with which we have determined phase relations of the RuO 2 phases and derived thermal equations of state (EoS) parameters for both Ru and RuO 2 . Rutile-structured RuO 2 was found to undergo two phase transformations, first at ~7 GPa to an orthorhombic structure and then above 12 GPa to a cubic structure. The phase boundary of the cubic phase was constrained for the first time at high pressure and temperature. We have derived a continuous Gibbs free energy expression for the tetragonal and orthorhombic phases of RuO 2 by fitting the second-order phase transition boundary and P-V-T data for both phases, using a model based on Landau theory. The transition between the orthorhombic and cubic phases was then used along with EoS terms derived for both phases to determine a Gibbs free energy expression for the cubic phase. We have used these data to calculate the oxygen fugacity of the Ru + O 2 = RuO 2 equilibrium, which we have parameterized as a single polynomial across the stability fields of all three phases of RuO 2 . The expression is log 10 f O 2 (Ru – RuO 2 ) = (7.782 – 0.00996P + 0.001932P 2 – 3.76 × 10 –5 P 3 ) + (–13 763 + 592P – 3.955P 2 )/T + (–1.05 × 10 6 – 4622P)/T 2 , which should be valid from room pressure up to 25 GPa and 773–2500 K, with an estimated uncertainty of 0.2 log units. Our calculated fO 2 is shown to be up to 1 log unit lower than estimates that use previous expressions or ignore EoS terms.

Armstrong, Katherine↗
DOE OSTI2025

Ab initio equation of state for vanadium

Accurate materials’ equations of state (EOS) are essential for understanding materials properties as well as for use in multiphysics simulations. In particular, hydrodynamics simulations are based on three fundamental conservation laws (mass, momentum and energy) that form an under-determined system of equations. The equation of state serves as an additional closure relation between thermodynamic variables for a given material that enables numerical hydrodynamics simulation. In this report, we focus on the development of an ab initio EOS for the body centered cubic (BCC) phase of Vanadium (V) for eventual integration into a multiphase EOS in the OpenSesame EOS database.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Thermodynamic Modeling of Complex Solid Solutions in the Lu-H-N System via Graph Neural Network Accelerated Monte Carlo Simulations

Metal hydrides are important across diverse applications, such as hydrogen storage, batteries, gas sensors, nuclear reactions, and high-temperature superconductivity. Previous computational studies of metal hydrides under extreme pressures, e.g., 𝑂⁡(10 2 ) ⁢GPa, usually treat them as stoichiometric compounds without considering interstitial lattice disorder. As pressures become more moderate in the 𝑂⁡(10 0 ) ⁢GPa and below range, hydrogen disorder at interstitial lattice sites becomes prominent, e.g., in the N-doped Lu hydride that was recently claimed superconducting near 1 GPa. Further adding compositional complexity from alloying and/or multielement interstitial occupation makes elucidating pressure- and temperature-dependent observables intractable by first-principles calculations alone. We therefore propose a lattice graph neural-network surrogate modeling approach to predict configuration- and pressure-dependent equation-of-state properties. Their efficiency permits Monte Carlo simulations to calculate Gibbs energies and pressure-dependent phase diagrams, thereby revealing insights into the synthesis conditions required for achieving desired phase equilibria. We demonstrate this concept for the compositionally complex cubic Lu(H,N,Va) 3 system where three constituents (hydrogen, nitrogen and vacancy) have disordered multielement interstitial occupancies and insights into pressure-dependent phase equilibria are critically needed, e.g., N-doping levels can significantly lower dehydrogenation temperatures and provide a new strategy to optimize hydrogen-storage alloys. This work can improve the thermodynamic understanding of the Lu-H-N system and help rational synthesis of N-doped Lu hydrides, but more generally demonstrates an efficient approach to model pressure-dependent thermodynamics of multicomponent solid solutions.

Monte Carlo methods↗
DOE OSTI2020

Shock compression of vanadium at extremes: Theory and experiment

Here, the equation of state (EOS) and shock compression of bulk vanadium were investigated using canonical ab initio molecular dynamic simulations, with experimental validation to 865 GPa from shock data collected at Sandia's Z Pulsed Power Facility. In simulations the phase space was sampled along isotherms ranging from 3000 K to 50 000 K, for densities between ρ = 3 and 15 g / cm 3 , with a focus on the liquid regime and the body-centered-cubic phase in the vicinity of the melting limit. The principal Hugoniot predicted from first principles is overall consistent with shock data, while it showed that current multiphase SESAME-type EOS for vanadium needed revision in the liquid regime. A more accurate SESAME EOS was developed using constraints from experiments and simulations. This work emphasizes the need to use a combined theoretical and experimental approach to develop high-fidelity EOS models for extreme conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1989

Non linear evolution of a second mode wave in supersonic boundary layers

Presented here are several direct simulations of one 2-D second mode perturbation wave, superimposed upon a prescribed mean flow. Periodicity is assumed in the streamwise direction (Fourier) and the variables are expanded in Chebyshev series in the direction normal to the flat plate. The code is fully explicit and is time advanced with a 3rd order Runge-Kutta scheme. The second mode wave (R delta prime = 8000), interacts with itself to generate higher streamwise harmonics. Physical parameters are chosen to maximize the linear growth rate at the prescribed Reynolds number. Initial results indicate that the nonlinear processes begin in the critical layer region and are the result of the cubic interactions in the momentum equations, rather than due to the higher streamwise harmonics. Analysis of the various terms in the momentum equations combined with numerical experiments in which various modes are artificially suppressed, lead to the conclusion that asymptotic methods will produce the saturated state in one or two order of magnitude less computer time than that required by the direct numerical simulations.

Erlebacher, Gordon↗
NASA NTRS1990

Second mode interactions in supersonic boundary layers

The nonlinear evolution of a two-dimensional second mode unstable wave in a Mach 4.5 wall-bounded flow is computed by solving the full time-dependent compressible Navier-Stokes equations. A highly accurate solution is obtained using spectral collocation methods. It is shown that departure from linearity first occurs in the critical layer due to the cubic nonlinearities in the momentum equation. This is a direct result of the large density perturbations in this regime. Time evolution studies of the growth rate as a function of normal distance from the plate suggests that the mode is evolving toward a nonlinear saturated state, and that this problem is possibly amenable to standard weakly nonlinear perturbation methods.

Erlebacher, Gordon↗
DOE OSTI2021

High-pressure synthesis and thermodynamic stability of PdH 1±ε up to 8 GPa

Palladium hydride alloys are superconductors and hydrogen storage materials. One synthesis route is compression of Pd to high pressure in a hydrogen-rich environment. Here we report the evolution of the unit cell volume of PdH x synthesized by compressing Pd in a pure H 2 medium to pressures from 0.2 to 8 GPa in a diamond anvil cell at room temperature. The volume of the face-centered cubic unit cell changes nonmonotonically with pressure, increasing upon compression from 0.2 to 1 GPa and decreasing upon compression from 1 to 8 GPa. Volume is reversible upon decompression and is independent of whether the sample was heated to 600 K at low pressure (P < 2 GPa). The x-ray diffraction data show no evidence for a phase transition between 0.2 and 8 GPa. The volume maximum at 1 GPa must be caused by progressive hydrogenation from 0 to 1 GPa. Assuming a pressure-volume-composition equation of state derived from previously published data, the [H]:[Pd] ratio in this study increases to a maximum value of x = 1 ± 0.02 at 2 ± 0.5 GPa and remains stable upon further compression to and from 8 GPa. These results add to a mounting body of evidence that PdH 1±ϵ is in thermodynamic equilibrium with pure H 2 at room temperature from 2 GPa to at least 8 GPa. Here, the simplest interpretation is that H atoms occupy all octahedral sites and no tetrahedral sites in face-centered cubic PdH 1.0 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Martensitic fcc-hcp transformation pathway in solid krypton and xenon and its effect on their equations of state

The martensitic transformation is a fundamental physical phenomenon at the origin of important industrial applications. However, the underlying microscopic mechanism, which is of critical importance to explain the outstanding mechanical properties of martensitic materials, is still not fully understood. This is because for most martensitic materials the transformation is a fast process that makes in situ studies extremely challenging. Noble solids krypton and xenon undergo a progressive pressure-induced face-centered cubic (fcc) to hexagonal close-packed (hcp) martensitic transition with a very wide coexistence domain. Here, we took advantage of this unique feature to study the detailed transformation progress at the atomic level by employing in situ x-ray diffraction and absorption spectroscopy. We evidenced a four-stage pathway and suggest that the lattice mismatch between the fcc and hcp forms plays a key role in the generation of strain. We also determined precisely the effect of the transformation on the compression behavior of these materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1975

Aluminum under high pressure. I - Equation of state

A curve of applied pressure versus lattice constant is calculated for single-crystal aluminum. It results from an application of the method of structural expansions for deriving the energies of simple metals, a method known to give reasonable results for the elastic constants even at second order in the effective electron-ion interaction. The latter is taken from Fermi-surface analysis, and it is verified that the extant face-centered cubic structure remains the preferred crystalline phase up to the highest pressures considered. Arguments are given to suggest that the curve should have reasonable a priori accuracy and can admit possible improvement if experimental data in the intermediate-pressure region can be provided to refine the (in principle) energy-dependent pseudopotential. At three megabars, the lattice constant is reduced by only 22 per cent; the ion cores at this pressure are still very well separated.

Friedli, C.↗
NASA NTRS1990

A comparison of internal energy calculation methods for diatomic molecules

Various methods of calculating the internal energy of diatomic molecules are studied. An accurate and efficient method for computing the eigenvalues of the vibrational Schroedinger equation for an arbitrary potential is developed. The method is based on a finite-element discretization using the cubic Lobatto element. A combination of spectrum slicing and the Laguerre algorithm is used to solve for the eigenvalues. A simple method to compute the quasi-bound states is presented. For N2 molecules, all vibrational-rotational states of eleven available electronic potentials are computed, and summed to obtain the exact internal energy function with temperature. The total computation required 314 seconds of CPU-time on NASA's Cray 2 computer. Various approximate models are discussed and compared with the exact numerical simulation. It is shown that the splitting of the macroscopic internal energy into separate electronic, rotational, and vibrational energies is not justified at high temperatures.

Liu, Yen↗
NASA NTRS1977

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of the nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The continuous cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and symptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗
NASA NTRS1975

Aluminum under high pressure: 1 equation of state

A curve of applied pressure P versus lattice constant a is calculated for single crystal aluminum. It results from an application of the method of structural expansions for deriving the energies of simple metals, a method known to give reasonable results for the elastic constants even at second order in the effective electron-ion interaction. The method is taken from Fermi surface analysis . This essentially experimental information is used to verify that the extant face-centered cubic structure remains the preferred crystalline phase up to the highest pressures considered. Arguments are given to suggest that the P versus a curve should have reasonable a priori accuracy, which may be improved if experimental data in the intermediate pressure region can be provided to refine the energy dependent pseudo-potential. At 3 megabars the lattice constant is reduced by only 22%; the ion cores at this pressure are still very well separated.

Friedli, C.↗
NASA NTRS1976

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗
DOE OSTI2020

Energy spectrum of two-particle scattering in a periodic box

We aim to compute the discrete energy spectrum for two-body scattering in a three-dimensional box under periodic boundary conditions. The spectrum in the center of mass is obtained by solving the Schödinger equation in a test potential using the Fourier basis. The focus is on how to project the spectrum into the various irreducible representations of the symmetry groups of the box. Four examples are given to show how the infinite-volume spectrum (including both bound and scattering states) is resolved in cubic or elongated boxes, and in systems with integer or half-integer total spin. Such a demonstration is a crucial step in relating the discrete spectrum in the box to the infinite-volume scattering phaseshifts via the Lüscher method.

Computer Science↗
NASA NTRS1985

Statistical theory of cubic Langmuir turbulence

The cubic direct interaction approximation is applied to a truncated (in Fourier space) version of the cubically nonlinear Schroedinger equation model of Langmuir physics. The results are compared (in the three-mode case) to those for an ensemble of numerical solutions of the dynamical equations with 10,000 different sets of Gaussianly distributed initial conditions. In the undriven, undamped case, the statistical theory (but not the ensemble) evolves to a state of thermal equilibrium. In the driven, damped case, the statistical theory appears to evolve to a state close to that corresponding to one of the limit cycles of the dynamical equations.

Sun, G.-Z.↗
DOE OSTI2025

HfZr_BCC_SolidSolution_128atoms_VASP6

We performed density functional theory (DFT) calculations for body-centered-cubic (BCC) structures with 128 lattices sites of solid solution binary alloys hafnium-zirconium (Hf-Zr). The electronic structures of alloys have been calculated using Vienna Ab initio Simulation Package (VASP). Within this package the DFT approach is used to reduce many-body Schrodinger equation to set of single particle Kohn-Sham (KS) equations. The generalized electronic exchange-correlation functional is described by generalized gradient approximation with the Perdew-Burke-Ernzerhof parametrization. The electron-ion interactions is described by pseudopotentials developed within the plane-wave basis projector augmented-wave (PAW) approach. These pseudopotentials are available at the VASP portal (http://cms.mpi.univie.ac.at/vasp/). Our calculations have been run with the pseudopotentials treating s and p semi-core states as valence in case for the elements Hf and Zr. The electronic densities and potentials are expanded over plane-waves with energy cutoff of 350 eV. 2x2x2 k-mesh and normal precision were used. The alloys were modeled by supercell containing 128 randomly distributed atoms. At initial step the atoms occupy perfect bcc lattice cites. This initial structure was optimized until energy changes less than 1e-6 eV, while forces acting on atoms don't exceed 1e-2 eV/angstrom. The electron-ion interaction is described by PAW pseudopotentials. The calculations have been collected by sampling chemical compositions across the entire compositional range. The chemical compositions have been sampled by progressively changing the number of atoms per constituent by 4. For each chemical composition of binaries and ternaries, the first-principle calculations have been run for 100 randomized arrangements of the constituents on the BCC lattice sites. We collected data for a total of 3,100 randomized atomic structures over 31 chemical compositions.

36 MATERIALS SCIENCE↗
NASA NTRS1975

An investigation of several numerical procedures for time-asymptotic compressible Navier-Stokes solutions

The status of an investigation of four numerical techniques for the time-dependent compressible Navier-Stokes equations is presented. Results for free shear layer calculations in the Reynolds number range from 1000 to 81000 indicate that a sequential alternating-direction implicit (ADI) finite-difference procedure requires longer computing times to reach steady state than a low-storage hopscotch finite-difference procedure. A finite-element method with cubic approximating functions was found to require excessive computer storage and computation times. A fourth method, an alternating-direction cubic spline technique which is still being tested, is also described.

Rudy, D. H.↗